Bifurcation analysis of a plant-herbivore model with toxin-determined functional response
type: Item
instance of: scholarly article
title: Bifurcation analysis of a plant-herbivore model with toxin-determined functional response
zbMATH Open document ID: 1165.34028
author: Rongsong Liu
author: Zhilan Feng
author: Huanping Zhu
author: Donald L. DeAngelis
published in: Journal of Differential Equations
publication date: 2008-07-10T00:00:00Z
review text: The authors study the dynamics of the system \[ \begin{aligned}\frac{dN}{dt}&=rN(1- {N}/{K})-C(N)P,\\ \frac{dP}{dt}&=BC(N)P-dP, \end{aligned} \] where \(C(N)=f(N)(1-f(N)/(4G)\) and \(f(N)\) is the Holling Type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically.
reviewed by: Xinyu Song
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 5299427
zbMATH Keywords: plant-herbivore model
zbMATH Keywords: stability
zbMATH Keywords: limit cycle
zbMATH Keywords: homoclinic bifurcation
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
full work available at URL: j.jde.2007.10.034
OpenAlex ID: W2163473248
cites work: Plant-herbivore interactions mediated by plant toxicity
cites work: Elements of applied bifurcation theory.
cites work: Modeling the impact of plant toxicity on plant-herbivore dynamics
cites work: Bifurcation Analysis of a Predator-Prey System Involving Group Defence
cites work: Bifurcation Analysis of a Predator-Prey System with Nonmonotonic Functional Response
DOI: 10.1016/J.JDE.2007.10.034
description: scientific article; zbMATH DE number 5299427